Towards Dynamic PET Reconstruction under Flow Conditions: Parameter Identification in a PDE Model

TL;DR

This paper develops a PDE-based model for PET imaging that incorporates flow conditions and proposes a method for estimating kinetic parameters from PET data using variational regularization and gradient-based algorithms.

Contribution

It introduces a novel PDE model including flow effects for PET reconstruction and formulates an inverse problem for parameter estimation with a new regularization approach.

Findings

Successful numerical tests demonstrate the feasibility of parameter identification.

The PDE model effectively captures flow effects in PET imaging.

Gradient-based algorithms efficiently solve the inverse problem.

Abstract

The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of transport-reaction-diffusion equations, which is able to include macroscopic flow properties in addition to the usual exchange between arteries, veins, and tissues. For this system we propose an inverse problem of estimating all relevant parameters from PET data. We interpret the parameter identification as a nonlinear inverse problem, for which we formulate and analyze variational regularization approaches. For the numerical solution we employ gradient-based methods and appropriate splitting methods, which are used to investigate some test cases.